Authors: Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Combinatorial groupoids, cubical complexes, and the lovász conjecture
Journal: Discrete and Computational Geometry
Volume: 41
Issue: 1
First page: 135
Last page: 161
Issue Date: 1-Jan-2009
Rank: M21
ISSN: 0179-5376
DOI: 10.1007/s00454-008-9062-1
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature", etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type invariant for cubical complexes, leading to a combinatorial "Theorema Egregium" for cubical complexes that are non-embeddable into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson-Kozlov-Lovász graph coloring results to more general statements about nondegenerate maps (colorings) of simplicial complexes and graphs.
Keywords: Combinatorial groupoids | Cubical complexes | Discrete differential geometry | Lovász conjecture
Publisher: Springer Link
Project: Serbian Ministry of Science and Technology, Grants no. 144014 and 144026

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